Substituting \(\tilde{\kappa }_\gamma \lesssim \sqrt{-\log \lambda }\)  into Theorem 5 in [1]}, we obtain that with \(\mathbb {P}_0^{(n)}\) -probability at least \(1-n^{-10}\)  it holds
\(\Vert \hat{f}_n-f_0\Vert _2\lesssim 2\Vert f_\lambda -f_0\Vert _\infty + \frac{8\sigma \sqrt{20\log n}\sqrt{-\log \lambda }}{\sqrt{n}},\) 
